The currently prevailing equilibrium-based approach to mechanism design suffers from a plurality of fundamental problems, and new conceptual frameworks are needed to solve or sufficiently alleviate them. In this paper, we put forward rational robustness, a new solution concept/implementation notion that is not equilibrium-based; prove its fundamental structural theorems; and compare it with prior notions. Our notion of implementation is specifically built so as to be robust against the problem of equilibrium selection. We prove it robust against other fundamental problems as well in different papers.